For the BM model in the chiral limit, Ref. [1]} showed that the bands around the CNP become exactly flat as long as \(v_{Dirac} = 0\) . Their argument is still valid when the relaxation induced pseudo-vector field \(\mathcal {A}\)  is present. To prove this statement, we consider the equation
\(\mathcal {D}(x) _{k, B}(x) = 0 \ , \) 
